Graphing InequalitiesEXAMPLE 1

Inequality Graph Verbal Phrase

a. y < 7

b. q 3

c. x > –5

d. h 212

All numbers less than 7

All numbers less than or equal to 3

All numbers greater than –5

All numbers greater than or equal to 2 1

2

Solving InequalitiesEXAMPLE 2

Solve the inequality. Then graph its solution.

x – 5 + 5 < 8 + 5

x < 13

Original inequality

Add 5 to each side.

Simplify.

x – 5 < 8

a. x – 5 < 8

Solving InequalitiesEXAMPLE 2

y – 7 –10

y – 7 + 7 – 10 + 7

y –3

Original inequality

Add 7 to each side.

Simplify.

b. y – 7 –10

Solving InequalitiesEXAMPLE 2

8 + m > 15

8 – 8 + m > 15 – 8

m > 7

Original inequality

Subtract 8 from each side.

Simplify.

c. 8 + m > 15

GUIDED PRACTICE for Examples 1 and 2

Graph and write a verbal phrase for the inequality.

1. z ≥ –1

SOLUTION

Inequality Graph Verbal Phrase

z ≥ –1 All numbers greater than or equal to –1–3 –2 –1 0 1

GUIDED PRACTICE for Examples 1 and 2

2. 4 > p

SOLUTION

Inequality Graph Verbal Phrase

4 > p All numbers less than 4. 2 3 4 5 6

GUIDED PRACTICE for Examples 1 and 2

3. k –3.5

SOLUTION

Inequality Graph Verbal Phrase

k –3.5 All numbers less than or equal to –3.5.

–5 –4 –3 –2 –1

GUIDED PRACTICE for Examples 1 and 2

4. m > 12

SOLUTION

Inequality Graph Verbal Phrase

12m > All numbers greater than .1

2–2 –1 0 1 2

GUIDED PRACTICE for Examples 1 and 2

5. x – 3 > –2

SOLUTION

Original inequality

Add 3 to each side.

Simplify.

x – 3 > – 2

x – 3 + 3> – 2+ 3

x > 1

Graph

GUIDED PRACTICE for Examples 1 and 2

6. 6 > t – 1

SOLUTION

Original inequality

Add 1 to each side.

Simplify.

6 > t – 1

6 + 1> t – 1+ 1

7 > t

Graph

GUIDED PRACTICE for Examples 1 and 2

7. 12 ≥ p + 14

SOLUTION

Original inequality

Subtract 14 from each side.

Simplify.

12 ≥ p + 14

– 14 ≥ p + 1412 – 14

≥ p–2

Graph

GUIDED PRACTICE for Examples 1 and 2

8. x + 5 < 10

SOLUTION

Original inequality

Subtract 5 from each side.

Simplify.

x + 5 < 10

x + 5 < 10– 5 –5x < 5

Graph x < 53 4 5 6 7

GUIDED PRACTICE for Examples 1 and 2

9. t + 9 6

SOLUTION

Original inequality

Subtract 9 from each side.

Simplify.

t + 9 6

t + 9 – 9 6 – 9

–3t

Graph

GUIDED PRACTICE for Examples 1 and 2

10. –4 < k –3

SOLUTION

Original inequality

Add 3 to each side.

Simplify.

–4 < k – 3

< k – 3 + 3–4 + 3< k–1

Graph